BE_MAP

To map values from nearby points to the centroids of boundary elements one may specify The results of this mapping may then be saved via Note: This functionality should currently only be used in conjunction with SAVE_BE_ITEM and BEmap(). Arguments :

• ExpressionToMap : This expression is evaluated for each point which is included in the mapping and its result is mapped to the BE, e.g. inline equation
• BeFilterExpression : Boundary elements are only included in the mapping if the result of this expression is bigger than zero, default : 1.0 (filtering off, i.e. consider all BEs)
• PointFilterExpression : Points are only included in the mapping if the result of this expression is bigger than zero, default : 1.0 (filtering off, i.e. consider all points)
• iMethod : Mapping method (see below), default : %EQN_BEmap_ClosestPoint%
• alphaKernel : Parameter to control the shape of the weighting function for %EQN_BEmap_Shephard%, default : 1

Mapping methods :

• %EQN_BEmap_ClosestPoint%: Take the value of the point which is closest to the boundary element centroid
• %EQN_BEmap_Shephard%: Take the Shephard interpolation (cf. projY() ) over all points located near the boundary element
• %EQN_BEmap_Sum%: Take the sum over all points located near the boundary element

Examples :

• Use default mapping method for BEs in any chamber and without any point filtering (to map the total pressure to the boundary)
  BE_MAP($BEmap1$) = ( [ Y%ind_p% + Y%ind_p_dyn% ] )
• Use default mapping method for BEs in chamber 1 and without any point filtering (to map the total pressure to the boundary)
  BE_MAP($BEmap1$) = ( [ Y%ind_p% + Y%ind_p_dyn% ], [ BEcham(0)= 1 ] )
• Choose mapping method for BEs of any chamber and without any point filtering (to map the total pressure to the boundary)
  BE_MAP($BEmap1$) = ( [ Y%ind_p% + Y%ind_p_dyn% ], 1.0, 1.0, %EQN_BEmap_ClosestPoint% )
• Choose mapping method for BEs in chamber 1 and filter out interior and free surface points from candidates for mapping (to map the total pressure to the boundary)
  BE_MAP($BEmap1$) = ( [ Y%ind_p% + Y%ind_p_dyn% ], equn{$EQN_BEmap_BeFilter$}, equn{$EQN_BEmap_PointFilter$}, %EQN_BEmap_Shephard%, 0.1 ) begin_equation{$EQN_BEmap_BeFilter$} if ( BEcham(0)= 1 ) :: 1.0 else :: -1.0 endif end_equation begin_equation{$EQN_BEmap_PointFilter$} if ( (Y%ind_kob% = %BND_none%) + (Y%ind_kob% = %BND_free%) ) :: -1.0 else :: 1.0 endif end_equation
• Same example but with an inline equation for the filtering
  BE_MAP($BEmap1$) = ( [ Y%ind_p% + Y%ind_p_dyn% ], [ BEcham(0)= 1 ], [ 1.0 - 2.0*( (Y%ind_kob% = %BND_none%) + (Y%ind_kob% = %BND_free%) ) ], %EQN_BEmap_Shephard%, 0.1 )
  Note : If this filtering is desired for all BE_MAP definitions, it can also be applied by setting BEmap_PointFilter_Version appropriately.

Basic algorithm :

• The BeFilterExpression is evaluated for each BE and BEs with a value <=0 are not considered for mapping
• For each BE which was not filtered out, the centroid location is determined
• As candidates for the mapping, all points in the h-ball around the centroid of the BE are determined
• All inactive (Y%ind_vol%<0.1) points and those not fulfilling the hardcoded filters according to BEmap_PointFilter_Version are removed from the list of candidates
• The PointFilterExpression is evaluated for each point and points with a value <=0 are removed from the list of candidates
• The mapping is done on the basis of the reduced list

Additional remarks :

• The default/fallback value can be changed via BEmap_DefaultValue